Abstract
We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner [Phys. Plasmas 20, 102117 (2013)] to allow for non-uniform density and temperature profiles. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al. [Phys. Plasmas 22, 112902 (2015)]. In one limit of the parameters, we recover the model of Kolotkov et al. [Phys. Plasmas 22, 112902 (2015)], while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive and give expressions for the pressure, density, temperature, and bulk-flow velocities of the equilibrium, discussing the differences from previous models. We also present some illustrative plots of the distribution function in velocity space.
Highlights
Force-free current sheets, with magnetic fields satisfying r Á B 1⁄4 0; (1) r  B 1⁄4 l0j; (2) j  B 1⁄4 0; (3)are appropriate for plasma modelling in, e.g., the solar atmosphere and planetary magnetospheres (e.g., Refs. 3–15)
We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner [Phys
We have presented a class of 1D strictly neutral Vlasov-Maxwell equilibrium distribution function (DF) for both linear and nonlinear force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, which are an extension of the DFs discussed by Abraham-Shrauner1 to account for non-uniformities in the temperature and density, whilst still maintaining a constant pressure, as is required for force-balance of the force-free equilibrium
Summary
Are appropriate for plasma modelling in, e.g., the solar atmosphere and planetary magnetospheres (e.g., Refs. 3–15). When a varies with the position r, the field is referred to as nonlinear force-free Such current sheets as described earlier can play a crucial role in, e.g., magnetic reconnection processes, for which it is often necessary to consider kinetic length scales (e.g., Ref. 16), since many astrophysical plasmas are approximately collisionless. The first solution for a nonlinear force-free field was found by Harrison and Neukirch (see Ref. 39) for the force-free Harris sheet, and these solutions were later extended by Kolotkov et al. to allow for non-uniform density and temperature profiles (with respect to the spatial coordinate). We will extend this class of DFs to include those consistent with non-uniform temperature and density profiles, using a similar approach used by Kolotkov et al. for the force-free Harris sheet.
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